Phenomenological quantum electrodynamics in periodic dielectric media

Probability and Entropy in Quantum Theory

“…How about other observables, uncertainty relations, and so many other notions that are central in standard quantum theory? Our brief answer (a more detailed discussion will appear in [18]) is that other observables are useful concepts in that they facilitate the description of complex experiments but, from our point of view, they are of only secondary importance and play no role at the foundational level. One can effectively build more complex detectors by modifying the setup (by introducing, e.g., magnetic fields or diffraction gratings) just prior to the final position detection at x f .…”

Dynamical diffraction theory for the parametric X-rays and coherent bremsstrahlung

“…At present there are a lot of experimental works in this field (see [15][16][17] for recent ones and references therein) and most of their results are in qualitative agreement with the predictions of [14] with a rather small deviation in their quantitative details. Essential contribution to the detailed analysis of this phenomenon was made in many theoretical works (for example, [18][19][20][21][22][23][24] and references therein).…”

Bloch theory of entangled photon generation in nonlinear photonic crystals

“…The two natural generalizations of the Coulomb gauge: ǫ(r)∇ · A = 0 and ∇ · (ǫ(r)A) = 0 lead to different quantization procedures. Here we summarize the results of Caticha and Caticha [12] who used the gauge ǫ(r)∇ · A = 0 to quantize the electro-magnetic field in a medium with periodic dielectric. They showed that the Hamiltonian is diagonal in the Bloch-wave basis and the creation operators for the field satisfy suitably modified commutation relations.…”

“…There are two natural generalizations of the Coulomb gauge: ǫ(r)∇ · A = 0 and ∇ · (ǫ(r)A) = 0 that reduce to the uniform dielectric Coulomb gauge ∇ · A = 0. In the gauge ǫ(r)∇ · A = 0, Maxwell's equations are given by [12]:…”

“…The present article is structured as follows: sections II and III discuss Bloch waves and their quantization in linear photonic crystals following essentially the work of Caticha and Caticha [12]. In section IV we derive an expression for the interaction Hamiltonian and the phasematching function that govern the down-conversion process in non-linear photonic crystals.…”